eS 
certain new forms of Thermo-Barometers. 5 
Supposing p—p, and g, to be determined by observation, 4, 
being neglected, or ¢,=7, the constant Y may be found from (2), 
viz. ' 
¥ Poth+ Ye 
i ag eg! ah op We 
ores s(p—Po)— 4) 
Again, solving equation (2) for the value of go, we get 
m=11A/ 4s(p—p.)~ + (spath+ Y\"— (p++) f, (5) 
which is the formula I have employed for graduating the baro- 
metrical scale by giving different values to po. 
By a similar mode of investigation we find, neglecting the 
pressure of the vapour of the liquid, 
ae {+458 a } 
el a Soar (pt+h+q)ztir. + (6) 
Here it will be observed that g, is very nearly in the ratio of 
t,—t, that is to say, the graduations on the thermometrical 
scale mn are very nearly uniform. Neglecting g, within the 
brackets, and solving the equality for g,, we find 
= (t,—2) (sp +h) roa FO) (7) 
. (14-458) { p++} 
This formula enables us to determine approximately the range 
of the thermometrical scale, having given the capacity of the 
flask, &c.; thus let ; 
a 1 
ar 180° e—-0; p=29'5, h=12, t= 62°; R=O27, 
then we find g,=5'8 ; again, for ¢,=32°, the other quantities 
being as before, we find g,= —5°8; therefore the range =11°6 
inches. 
In like manner formula (3) enables us to determine approxi- 
mately the range of the barometrical scale, having given the 
range of the mercurial barometer; thus let p,=31 for the lower 
part of the scale, and p,=28 for the upper part, the other quan- 
tities being as before, then we find the entire range =10 inches 
nearly. Hence the length of the tube should not be less than 
21:6 inches. The range of this instrument, indicating atmo- 
spheric change of pressure, is about three times that of the 
common barometer. 
The instrument which I shall now describe has a range of 73 
times that of the common barometer, and is at the same time 
strictly mathematical as regards the principle of construction, 
